Nah, the "SS" and "HD" bits refers to how each storage disk reads data. HDDs use hard metal disks to read & write data, hence it got the misnomer hard disk drive. SSDs use solid state flash memory to read & write data, hence it being called a solid state drive.

If you want the general category, you'd want to say "storage drive" specifically since if you say "drive", that can also refer to an optical drive (AKA the CD slot) or a USB drive (AKA flash/thumb drives).